Question

Find the range f(x)=x^3-3 with domain[-1,2]

Answer 1

f(x)=

use the method of graph to find the range of given function

when f(x) is replaced with {f(x)-t} than the graph shifts down by t units

to draw the graph of {x^3-3}

first draw the graph of x^3 then shifts it down by 3 units

the range of the function will be [f(-1),f(2)]

f(-1)=(-4) f(2)=5

therefore range of the function will be [(-4),5]

note:the above function is monotonically increasing therefore we can directly find the range of the function by putting the interval of domain

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